An object is placed in front of a concave mirror of focal length 20 cm. The image formed is three times the size of the object. Calculate two possible distances of the object from the mirror.
We can use the mirror equation to solve this problem. The mirror equation is:
1/f = 1/di + 1/do
where:
f = focal length of the mirror (= -20 cm for a concave mirror)
di = distance of the image from the mirror
do = distance of the object from the mirror
Given that the image formed is three times the size of the object, we can conclude that di/do = 3.
Substituting these values into the mirror equation, we get:
1/-20 = 1/di + 1/do
-1/20 = 1/di + 1/do
-1/20 = (do + di)/(do*di)
-do*di/20 = do + di
Since di/do = 3, we can substitute di = 3do into the equation:
-do*(3do)/20 = do + 3do
-3do^2/20 = 4do
-do^2/20 = 4
do^2 = -80
This is not a possible solution, as the square of a real number cannot be negative.
Therefore, there are no real solutions to this problem.